Meet the top quark, the heavyweight champion of the subatomic world, tipping the scales at a mass comparable to a single tungsten atom. Unlike its lighter counterparts, this elusive particle has a flair for the dramatic by boasting the shortest lifespan of all quarks and the unique ability to be measured as a "free" quark, for a fleeting moment, before decaying. With the discovery of the Higgs boson through proton-proton collisions at the Large Hadron Collider (LHC) in 2012, and no sign of any physics beyond the Standard Model (SM), measurements of the top quark provide an alternate approach to understanding and testing the SM. This thesis will present two measurements of the top quark at a centre-of-mass energy of 5.02 TeV, using 257 pb(-1) of proton-proton collision data collected by the ATLAS detector. The first is a tt ̅ (top-quark pair production) cross-section measurement that is used to improve our understanding of the internal structure of the proton. The second is a search for t-channel single-top-quark production. The pair production cross-section was measured individually in both the dilepton and single-lepton channels of the tt ̅ decay before being combined. The measurement in the single-lepton channel is also currently the most precise measurement of the top-quark pair production cross-section by the ATLAS Collaboration to date. The t-channel cross-section is measured in the semi-leptonic decay of the top quark and is the first observation of this process at a centre-of-mass energy of 5.02 TeV.